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Create systems of linear equations with each possible number of solutions.?
Create systems of linear equations with each possible number of solutions.
y=x+3, y=-2x-2; y=x+4, y=x+4; y=2x-6, y=2x+3
Explain the equations, and if there is other ways to write them. Is
it possible for the equations to look completely different but the solution
set still be "infinitely many"?
1 Answer
- Meng tianLv 78 years agoFavorite Answer
y = x + 3
y = -2x - 2
The equations are both linear and the system is consistent, so there is exactly 1 solution.
y = x + 4
y = x + 4
There is only 1 unique equation, and as such, there are infinitely many solutions.
y = 2x - 6
y = 2x + 3
The equations are linear, but the system is inconsistent, so there are no solutions.
It is possible for 2 equations to look different at first glance, yet still have infinitely many solutions. For example, y = x + 4 and 3y = 3x + 12 looks different, but they are essentially the same and will result in infinitely many solutions when put together.